Persistent random walks with finite velocities are powerful models describing chemotaxis [1]}, [2]}, [3]}, [4]}, organism movement and searching strategies [5]}, [6]}, [7]}, intracellular transport [8]} and cell motility [9]}, [10]}.
Stochastic cell movement plays a major role in embryonic morphogenesis, wound healing and tumor
cell proliferation [11]}. The modeling
of cell and bacteria migration towards a favorable environment is usually based on “velocity-jump” models describing self-propelled motion with the
runs and tumbles. Finite velocities and inertial resistance to changes in direction make these random walks physically well motivated since random walkers in nature cannot instantaneously jump to different states.
The collective behavior of cells and various organisms is another rapidly growing area of
active matter research [12]}, [13]}. Various hyperbolic models involving nonlinear partial
differential equations (PDEs) for the population densities have been used for analysis of spatio-temporal patterns describing the chemical and social interactions of organisms [14]}, [15]}, [16]}, [17]}, [18]}.
